A device for cleaning workpiece supports is described, for example in WO 2004/043638 A1. The described device for removing contamination requires manual advancement along the supporting strip. In the case of machines used for thermal cutting process, metal that has been melted by a laser cutting beam, for example, can flow down onto the workpiece support. Slag deposits can form on portions of the supporting strips, and as a result, the workpiece may no longer be evenly supported on the supporting strips.